After Scaife tied the game at six with a 3-pointer left wing, Kyla Whitehead put the Flyers on top with a trey from the other side of the floor.
They recorded assists on eight of their first 10 field goals and led by as many as 20 in the second quarter.
The Billikens went on an 11-0 run to draw within nine points with 1:59 left in the second quarter but Whitehead’s layup gave UD a 35-24 lead at the break.
Dayton shot 45.2 percent in the first half while SLU made just 32.1 percent of its shots from the floor.
The visitors were hot from downtown, though, making 5 of 6 from 3-point range while UD was 6-for-10.
Scaife had 14 points to lead all scorers in the first half while Ciaja Harbison had eight to lead Saint Louis.
Both teams struggled to find the mark in the third quarter, making a combined 6 of 31 shots, and the Flyers were able to take their 11-point lead into the final stanza.
>>QUARTERFINALS: Flyers start hot, hold on for win over Richmond
Scaife got the scoring started in the fourth quarter with a break-away layup that stretched Dayton’s lead back to 13 points.
SLU hung tough, though, forcing four turnovers in the first four minutes of the fourth quarter and cutting the Dayton lead to 50-42 when Dayton coach Shauna Green called timeout with 5:23 to go.
The Flyers scored seven of the next nine points to regain control after that.
Erin Whalen hit a short jumper after Jenna Giacone kept the play alive with an offensive rebound, and Scaife hit two free throws and a 3-pointer to put the Flyers back up by 11.
The championship game of the Atlantic 10 women’s basketball tournament is set to tip at noon Sunday at UD Arena.